Here is the full list of all 18 Rhythium achievements.
Beat any song with a C or higher
Beat any song with a B or higher
Beat any song with an A or higher
Beat any song with an S or higher
You perfected a song with an SS!
Beat any 5 songs with a C or higher
Beat any 5 songs with a B or higher
Beat any 5 songs with an A or higher
Beat any 5 songs with an S or higher
You perfected 5 songs with an SS!
Beat any 10 songs with a C or higher
Beat any 10 songs with a B or higher
Beat any 10 songs with an A or higher
Beat any 10 songs with an S or higher
You perfected 10 songs with an SS!
Hit 50,000 notes total
Play 50 custom songs
Complete a song with max multiplier with mods (x1.25)